A note on the stability and boundedness results of solutions of certain fourth order differential equations

Abstract

The purpose of this paper is to investigate the asymptotic stability of the zero solution of x (4)+ϕ( x ̈ ) x ⃛ +f(x, x ̇ ) x ̈ +g( x ̇ )+h(x)=0 with p≡0 and the boundedness of all solutions of x (4)+ϕ( x ̈ ) x ⃛ +f(x, x ̇ ) x ̈ +g( x ̇ )+h(x)=0 with p≠0. The results obtained here revise the results in [Demonstratio Math. 31(1) (1998) 87] and improve and includes some results in the relevant literature [J. Math. Anal. Appl. 5 (1962) 136; J. London Math. Soc. 37 (1962) 28; J. London Math. Soc. 42 (1967) 51; SIAM. J. Math. Anal. 1 (1970) 27; Int. J. Control. 69(2) (1998) 353].